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Thread: Fractal-oscillation attraction

  1. #1 Fractal-oscillation attraction 
    Administrator KALSTER's Avatar
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    Ok, time for another out-there question. :wink:

    First, a quote from the Wiki page on Fractals:

    A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. The term was coined by BenoƮt Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured."

    A fractal often has the following features:
    It has a fine structure at arbitrarily small scales.
    It is too irregular to be easily described in traditional Euclidean geometric language.
    It is self-similar (at least approximately or stochastically).
    It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
    It has a simple and recursive definition.


    And an example:


    The Mandelbrot set is a famous example of a fractal.


    A closer view of the Mandelbrot set.

    Now, imagine a 3D version of a fractal created by an oscillating disturbance at its centre. The oscillation means that the orientation of the fractal (into its mirror image) changes with a certain frequency and that the speed at which the newly created fractal moves away from its source is governed by the medium of propegation it finds itself in. The shape, size and type of the fractal is determined by the particular shape, size and type of the disturbance. It is possible for the shape of two fractals to be equal in every way except for the orientation being in the opposite direction (i.e. it points outward instead of inward).

    My question is: Is it possible for the interaction between these two fractals, equal except for orientation, to exert an attractive force on each other? Would two of the exact same fractals then exert a repulsive force on each other?


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  3. #2  
    Forum Masters Degree bit4bit's Avatar
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    I think fractals generally are just considered purely geometrically, and although they can be seen in nature (according to wiki they're only approximate, having finite self-similarity), I don't think they can be tied to being responsible for any physical force. Also, I'm not sure exactly what you meant by fractals 'oscillating.'


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  4. #3  
    Administrator KALSTER's Avatar
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    Quote Originally Posted by bit4bit
    I think fractals generally are just considered purely geometrically, and although they can be seen in nature (according to wiki they're only approximate, having finite self-similarity), I don't think they can be tied to being responsible for any physical force. Also, I'm not sure exactly what you meant by fractals 'oscillating.'
    Well, I was thinking of fractals in the form of self-similar reducing eddies in a medium, that is, reducing as the energy is dissipated with distance by forming multitudes of smaller and similar eddies (if that makes sense). This hypothetical medium would have no internal friction as one would expect from water, say.
    By oscillating I mean that they form mirror images of each other along an axis running through the source, roughly in the same manner a sine-wave would.
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  5. #4  
    Forum Masters Degree bit4bit's Avatar
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    Are you talking about eddy currents in a fluid then? If you have two identical eddy currents that were opposite to each other, then the forces causing the eddies would be in equillibrium. I don't really get what you're syaing.
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  6. #5  
    Administrator KALSTER's Avatar
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    Yeh, I usually have trouble setting up effective analogies :wink:

    For simplification, think of a wave-form being emitted around an axis of symmetry, similar to a sine wave, but instead of the regular positive and negative curves, you have (alternating between each side of the axis) spirals/eddies curling in the direction of the disturbance. This single arm comes into contact with the arm of another disturbance. The direction of rotation of the spirals/eddies will clash head-on with the spirals/eddies of the other arm. Now extrapolate this to a 3D situation with large numbers of arms from the two disturbances interacting with each other. The disturbances should be attracted to each other, no?
    Disclaimer: I do not declare myself to be an expert on ANY subject. If I state something as fact that is obviously wrong, please don't hesitate to correct me. I welcome such corrections in an attempt to be as truthful and accurate as possible.

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  7. #6 Re: Fractal-oscillation attraction 
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    Quote Originally Posted by KALSTER
    Now, imagine a 3D version of a fractal created by an oscillating disturbance at its centre.
    Isn't a fractal image only a plot representation of complex numbers resulting from a recursive formula with the real and imaginary part being the two coordinates? Shouldn't such a fractal always be 2D?
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  8. #7 Re: Fractal-oscillation attraction 
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    Quote Originally Posted by Dishmaster
    Quote Originally Posted by KALSTER
    Now, imagine a 3D version of a fractal created by an oscillating disturbance at its centre.
    Isn't a fractal image only a plot representation of complex numbers resulting from a recursive formula with the real and imaginary part being the two coordinates? Shouldn't such a fractal always be 2D?
    I came across this.

    Here is an excerpt from it:
    Attractor


    Visual example of an attractor (from another site I found):




    An attractor is a set to which a dynamical system evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.


    And from the Wiki page on Fractals:

    Approximate fractals are easily found in nature. These objects display self-similar structure over an extended, but finite, scale range. Examples include clouds, snow flakes, crystals, mountain ranges, lightning, river networks, cauliflower or broccoli, and systems of blood vessels and pulmonary vessels. Coastlines may be loosely considered fractal in nature.
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  9. #8 Re: Fractal-oscillation attraction 
    Forum Professor serpicojr's Avatar
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    Quote Originally Posted by Dishmaster
    Isn't a fractal image only a plot representation of complex numbers resulting from a recursive formula with the real and imaginary part being the two coordinates? Shouldn't such a fractal always be 2D?
    Here's a pretty famous "3D" fractal:

    http://en.wikipedia.org/wiki/Menger_sponge
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  10. #9  
    Moderator Moderator Dishmaster's Avatar
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    Thank you for your replies. Beautiful examples. I am not so familiar these topics. So forgive my lack of knowledge. It seems that the representation by complex numbers is only a subset of possibilities to produce fractals.

    Cheers! :-D
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  11. #10  
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    Quote Originally Posted by Dishmaster
    Thank you for your replies. Beautiful examples. I am not so familiar these topics. So forgive my lack of knowledge. It seems that the representation by complex numbers is only a subset of possibilities to produce fractals.

    Cheers! :-D
    To be sure, I don't know any of the math involved either, only their definition. :wink:

    Ok, so assuming that nature can not be infinitely reduced (the space-time fabic for instance), I guess this fractal would have to terminate after a certain number of instances. Maybe even straight down to the planck length.

    Whatever the case may be, does anyone have an oppinion as to the possibility of the interaction between fractals in nature resulting in an attractive or repulsive net force?
    Disclaimer: I do not declare myself to be an expert on ANY subject. If I state something as fact that is obviously wrong, please don't hesitate to correct me. I welcome such corrections in an attempt to be as truthful and accurate as possible.

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  12. #11  
    Administrator KALSTER's Avatar
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    I made this same thread on another forum and it got Really Interesting over there!
    Disclaimer: I do not declare myself to be an expert on ANY subject. If I state something as fact that is obviously wrong, please don't hesitate to correct me. I welcome such corrections in an attempt to be as truthful and accurate as possible.

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  13. #12  
    Forum Professor serpicojr's Avatar
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    We're so uncool.
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  14. #13  
    Administrator KALSTER's Avatar
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    Quote Originally Posted by serpicojr
    We're so uncool.
    Nah, this is home :wink: I guess they don't know me over there too well, so some of them might actually read my out-there stuff! And I think this line of thinking I have been employing for my hypothesis in progress might actually be getting somewhere!
    Disclaimer: I do not declare myself to be an expert on ANY subject. If I state something as fact that is obviously wrong, please don't hesitate to correct me. I welcome such corrections in an attempt to be as truthful and accurate as possible.

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  15. #14  
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    Now, imagine a 3D version of a fractal created by an oscillating disturbance at its centre.
    How can this be done?
    Beyond Equations,

    Pritish
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  16. #15  
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    Quote Originally Posted by PritishKamat
    Now, imagine a 3D version of a fractal created by an oscillating disturbance at its centre.
    How can this be done?
    I posted my initial thoughts on this and three other forums, with THIS one being among the most productive, or you can find the one on this forum HERE. Basically the premise is that there is an aether, that particles are complex and oscillating wave-bundles and then this thread where I propose that three of the four forces coupled to particles are distortion extensions of sorts of the space-time fabric/aether. One of the requirements for this model to work is that the aether has to behave like a superfluid, i.e. there is no internal friction and zero viscosity. I did some reading on Fractals and thought that they could be the perfect mechanism whereby attraction/repulsion could take place as the force needs to be pretty consistent under varying conditions. I imagined that in a 3D environment eddies could have a fractal character and provide the mechanical dynamics needed for forces to be exhibited. Then in the last few days when reading through the Wiki article on Superfluids, I came upon a section where it is described how superfluids can manifest quantized vortices under certain conditions, which I quoted earlier. This was almost too good to be true!

    Originally I just imagined that a big “tug-and-release” on the space-time fabric would shape the particle wave-bundle and then it would stay as is, but during a discussion with MitcelMcCain he suggested that under zero friction conditions the particle would not stay there, but would unfold and then refold in the opposite direction without losing energy. This would create an oscillation with a signature frequency for each particle. It is from here that I thought that such an oscillation would cause dynamic disturbances in the surrounding space, similar to gripping a piece of cloth in the middle and twisting.
    Disclaimer: I do not declare myself to be an expert on ANY subject. If I state something as fact that is obviously wrong, please don't hesitate to correct me. I welcome such corrections in an attempt to be as truthful and accurate as possible.

    "Gullibility kills" - Carl Sagan
    "All people know the same truth. Our lives consist of how we chose to distort it." - Harry Block
    "It is the mark of an educated mind to be able to entertain a thought without accepting it." - Aristotle
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